Algebraic groups | Lie groups

Bruhat decomposition

In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) G = BWB of certain algebraic groups G into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices—but with exceptional cases. It is related to the Schubert cell decomposition of flag varieties: see Weyl group for this. More generally, any group with a (B, N) pair has a Bruhat decomposition. (Wikipedia).

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Related pages

Length function | Algebraically closed field | Dynkin diagram | Classical group | Borel subgroup | Symmetric group | Determinant | Double coset | General linear group | Armand Borel | Poincaré duality | Cluster algebra | Connected space | Weyl group | Fundamental class | Reductive group | Special linear group | Claude Chevalley | Algebraic group | Nicolas Bourbaki | Birkhoff factorization | Longest element of a Coxeter group | (B, N) pair